薄片法求體積(2)
Author: 藍邦偉　老師

單位向量

座標軸

Start

x

y

z

$ O $

$焦距為%v$

$x=%v$

1

2

$ 正三角形 $

$ 正方形 $

$ 薄片法求體積(2) $

O = (6.831420147211042, 0.3456945350253491)
β = 1.3089969389957472 rad (slider from 0 to 6.283185307179586, step 0.1*°)
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
α = 0.9599310885968813 rad (slider from 0 to 6.283185307179586, step 0.1*°)
X_{unit}: O + (cos(α), sin(α) * cos(β))
u = Vector(O, X_{unit})
Y_{unit}: O + (-1 * sin(α), cos(α) * cos(β))
v = Vector(O, Y_{unit})
L = 6 (slider from 1 to 10, step 1)
yy = Vector(O - L * v, O + L * v)
zz = Vector(O - L * w, O + L * w)
xx = Vector(O - L * u, O + L * u)
c_1 = false
d = false
Q_2: 0.2 * Corner[2] + 0.8 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
g = Segment(Q_2, Q_3)
poly1, h, q_1, q_4, i = Polygon(Corner[1], Q_2, Q_3, Corner[4])
c = 2 (slider from 1 to 5, step 1)
t = 3.6 (slider from 0 to 8, step 0.01)
A_0: O + t * u
A_2: O + t * u - 2 * sqrt(c * t) * v
A_3: A_0 + sqrt(3) * sqrt(c * t) * w
e = true
k = false
a = CurveCartesian(x(O + c * t^(2) * u + 2 * c * t * v), y(O + c * t^(2) * u + 2 * c * t * v), t, -5, 5)
A_1: O + t * u + 2 * sqrt(c * t) * v
poly3, a_4, a_5, a_6 = Polygon(A_3, A_2, A_1)
List1 = Sequence(O + t * u + sqrt(3) * sqrt(c * t) * w, t, 0, 8, 0.5)
List2 = Sequence(O + t * u - 2 * sqrt(c * t) * v, t, 0, 8, 0.5)
List3 = Sequence(O + t * u + 2 * sqrt(c * t) * v, t, 0, 8, 0.5)
ListT = Sequence(Polygon[Element[List1, k], Element[List2, k], Element[List3, k]], k, 1, 20, 1)
b = CurveCartesian(x(O + t * u + sqrt(3) * sqrt(c * t) * w), y(O + t * u + sqrt(3) * sqrt(c * t) * w), t, 0, 8)
B_1: O + 8 * u - 2 * sqrt(c * 8) * v
B_2: O + 8 * u + 2 * sqrt(c * 8) * v
f = Line(B_1, B_2)
C_1: O + t * u + 2 * sqrt(c * t) * v + 4 * sqrt(c * t) * w
C_2: O + t * u - 2 * sqrt(c * t) * v + 4 * sqrt(c * t) * w
poly2, c_2, a_1, a_2, c_3 = Polygon(C_1, A_1, A_2, C_2)
j = CurveCartesian(x(O + t * u - 2 * sqrt(c * t) * v + 4 * sqrt(c * t) * w), y(O + t * u - 2 * sqrt(c * t) * v + 4 * sqrt(c * t) * w), t, 0, 8)
l = CurveCartesian(x(O + t * u + 2 * sqrt(c * t) * v + 4 * sqrt(c * t) * w), y(O + t * u + 2 * sqrt(c * t) * v + 4 * sqrt(c * t) * w), t, 0, 8)
List4 = Sequence(O + t * u + 2 * sqrt(c * t) * v + 4 * sqrt(c * t) * w, t, 0, 8, 0.5)
List5 = Sequence(O + t * u - 2 * sqrt(c * t) * v + 4 * sqrt(c * t) * w, t, 0, 8, 0.5)
ListS = Sequence(Polygon[Element[List2, k], Element[List3, k], Element[List4, k], Element[List5, k]], k, 0, 17, 0.5)